CN106684854A - A risk analysis method for active distribution network voltage crossing limit based on node equivalence - Google Patents

Abstract

The present invention provides a node equivalent-based active distribution network voltage transgression risk analysis method, comprising the following steps: establishing an active distribution network equivalent state model; calculating the voltage transgression probability of each equivalent node in a discrete state; Calculate the voltage limit probability under the actual operating state of the node load. The invention utilizes the characteristics that the number of equivalent state parameters of each node after simplification is small and can represent the comprehensive effect of various operating states of the system on the node voltage, and proposes that each equivalent node in the active distribution network can be selected according to the characteristics of the node to be discrete Offline calculation of the status and generation of corresponding databases to provide reference calculation samples for online rapid analysis; effectively solve the problem of quickly and accurately calculating the voltage over-limit probability of each node of the active distribution network during actual operation; it is conducive to fast online analysis and calculation, and With high accuracy.

Description

A risk analysis method for active distribution network voltage crossing limit based on node equivalence

technical field

The invention relates to an analysis method, in particular to a node equivalent-based risk analysis method for voltage over-limit of an active distribution network.

Background technique

With the increasing energy and environmental problems, new energy and renewable energy power generation technologies have developed rapidly, and distributed power generation technologies that promote the use of renewable energy and effectively complement centralized power generation have also been more and more widely used. As an important representative of distributed power generation technology, in the active distribution network, the photovoltaic power generation system is the most prominent in the development of advantages such as small scale, easy installation, decentralization and flexibility, and clean energy. However, as the penetration rate of photovoltaic systems continues to increase, due to its greater impact on the environment, the power output has strong randomness and volatility, which brings a series of power quality problems to users. In particular, high-penetration photovoltaic systems may cause overvoltage conditions in active distribution networks, making the risk of voltage violations more prominent and complex.

For the active distribution network with dual uncertain factors of load and photovoltaic power generation, the risk analysis and calculation of voltage violation has been transformed from a deterministic calculation problem to a random calculation problem, and the traditional deterministic power flow is replaced by a probabilistic power flow Calculation The analysis and calculation of the model with uncertainty is completed. This method fully considers the characteristics of the load and the power probability model of the photovoltaic system. Compared with the discrete values corresponding to the special points of the deterministic model, it can better characterize the overall shape characteristics of the voltage in possible values. The methods of solving probability power flow mainly include simulation method, analytical method and approximate method. Among them, the simulation method simulates various uncertain factors and their combinations through a large number of samples. In theory, it can use an accurate nonlinear power flow calculation method, and can consider the correlation between uncertain factors, so the accuracy of calculation The least restrictive. However, it has problems such as excessive calculation and long time consumption, which restrict its application in actual operation. The analytical method requires a large number of convolution operations on the basis of approximate linearization. The approximation method can directly obtain the probability and statistical characteristics of the objective function, but there are certain errors for the probability distribution types other than the normal probability distribution.

In the active distribution network, if the multidimensional uncertain model of each node load and multiple photovoltaic units is considered, it cannot be guaranteed that the voltage distribution law of the node voltage must satisfy the normal distribution. Therefore, no matter whether the more accurate simulation method is adopted, or the analytical method and approximate method with certain limitations can not avoid the defects of excessive calculation amount or large calculation error.

Contents of the invention

In order to overcome the deficiencies of the above-mentioned prior art, the present invention provides a method for risk analysis of active distribution network voltage exceeding the limit based on node equivalents, which fully considers the random characteristics of loads and distributed power sources, and performs active distribution network voltage exceeding In the actual operation, the power quality of the active distribution network is evaluated, and the corresponding control is carried out according to the evaluation and analysis results.

In order to realize the above-mentioned purpose of the invention, the present invention takes the following technical solutions:

The present invention provides a node equivalent-based active distribution network voltage transgression risk analysis method, the analysis method includes the following steps:

Step 1: Establish the node equivalent load probability model, and combine the photovoltaic system light intensity stochastic model to establish the equivalent state model of the active distribution network;

Step 2: Perform stochastic power flow calculation on the discrete state of each equivalent node, and calculate the voltage limit probability of each equivalent node in the discrete state according to the stochastic power flow result;

Step 3: Find the adjacent values of the node equivalent state parameters in the actual operating state of the node load in the offline database, and calculate the voltage limit probability under the actual operating state of the node load.

Described step 1 comprises the following steps:

Step 1-1: Select the maximum load state of each node in the active distribution network, and establish a node equivalent load probability model;

Step 1-2: Combining with the stochastic model of photovoltaic system light intensity, establish the equivalent state model of active distribution network.

In the step 1-1, establishing a node equivalent load probability model includes:

Assuming that node h and node k are any two adjacent nodes, node h and node k form a line hk, there are:

in, Denotes the voltage drop vector between node h and node k, Represents the current vector of the line hk, R _hk represents the resistance of the line hk, X _hk represents the reactance of the line hk, Indicates the node k potential vector, Indicates the complex power flowing through node k;

Neglecting the line loss, then Expressed as:

Among them, j=1,2,...,N _k , N _k represents the collection of all nodes after node k in the active distribution network viewed from the head end of the line hk, Indicates the load complex power of node j;

suppose Represents the rated voltage vector of the active distribution network, E _n represents the rated voltage vector magnitude of the active distribution network, so Also expressed as:

in, express the conjugate of Indicates the impedance vector of the line hk;

Therefore, for any equivalent node i in the active distribution network, there are:

in, Indicates the voltage drop vector between the equivalent node i and the bus in the active distribution network, L _i represents the set of all lines between the equivalent node i and the bus in the active distribution network, express the conjugate;

If there is only equivalent node i with load in the active distribution network, then It can also be expressed as:

in, Indicates the sum of the impedance between the equivalent node i and the bus in the active distribution network, express the conjugate of Indicates the complex power of the equivalent node i;

Due to the random fluctuation of the load power, the short-term fluctuations of active power and reactive power of each node load satisfy the normal distribution, so it can be obtained from equations (5) and (6):

and have:

Among them, a _hk means The real part of b _hk means The imaginary part of ; P _k represents the sum of active loads of all nodes after node k in the active distribution network, namely P _j represents the active load of node j; Q _k represents the sum of reactive loads of all nodes after node k in the active distribution network, namely Q _j represents the reactive load of node j;

Then by the linear law of normal distribution we can get:

Among them, E(P _eqi ) represents the equivalent active load expectation of equivalent node i, E(Q _eqi ) represents the equivalent reactive load expectation of equivalent node i, P _eqi represents the equivalent active load of equivalent node i, Q _eqi represents the equivalent reactive load of equivalent node i, E(P _j ) represents the expected active load of node j, and E(Q _j ) represents the expected reactive load of node j;

Since formula (10) does not satisfy the independence of random variables, it is transformed into:

and have:

Wherein, N _node represents the set of load nodes in the active distribution network, m=1, 2,..., N _node ; express the conjugate of Represents the complex power of the load node m; L _m represents the collection of all lines between the bus and the _intersection point when the line where the load node m is located and the nearest intersection point to the load node m exists; P _m represents the active load of the load node m, Q _m represents the reactive load of load node m; c _m and d _m represent The real and imaginary parts of ;

So there are:

Among them, σ(P _eqi ) represents the standard deviation of the equivalent active load of the equivalent node i, σ(Q _eqi ) represents the standard deviation of the equivalent reactive load of the equivalent node i, and D(P _eqi ) represents the standard deviation of the equivalent node i Equivalent active load variance, D(Q _eqi ) represents the equivalent reactive load variance of equivalent node i, D(P _m ) represents the active load variance of load node m, D(Q _m ) represents the reactive power of load node m load variance.

In the step 1-2, in the stochastic model of the photovoltaic system light intensity, the sun light intensity obeys the Beta distribution, and the sun light intensity expectation is represented by E(S), so the equivalent state model of the active distribution network is expressed as:

{E(S),E(P _eqi ),σ(P _eqi ),E(Q _eqi ),σ(Q _eqi )} (14)

Among them, σ(P _eqi ) represents the standard deviation of the equivalent active load of the equivalent node i, σ(Q _eqi ) represents the standard deviation of the equivalent reactive load of the equivalent node i, and E(P _eqi ) represents the standard deviation of the equivalent node i The equivalent active load expectation, E(Q _eqi ) represents the equivalent reactive load expectation of the equivalent node i.

Described step 2 comprises the following steps:

Step 2-1: Select the discrete state of each equivalent node in the active distribution network;

Step 2-2: Use Latin hypercube sampling to perform stochastic power flow calculations on the discrete states of each equivalent node, and obtain stochastic power flow results;

Step 2-3: According to the results of random power flow, and using the theorem of large numbers to calculate the probability of voltage exceeding the limit of each equivalent node in a discrete state;

Step 2-4: Save the voltage limit probability in the discrete state of each equivalent node to the offline database.

Described step 3 comprises the following steps:

Step 3-1: Obtain the actual operating status of each node load and the actual operating status of the photovoltaic system;

Step 3-2: Find the adjacent value of the node equivalent state parameter under the actual running state of the node load in the offline database;

Step 3-3: Use the multidimensional Lagrange interpolation method to calculate the probability of voltage exceeding the limit under the actual operating state of the node load, and analyze the risk of voltage exceeding the limit.

In the step 3-2, the node equivalent state parameters include the solar illumination intensity expectation E(S), the equivalent active load expectation E(P _eqi ) of the equivalent node i, and the equivalent active load standard deviation of the equivalent node i σ(P _eqi ), the equivalent reactive load expectation E(Q _eqi ) of the equivalent node i and the standard deviation σ(Q _eqi ) of the equivalent reactive load of the equivalent node i.

Said step 3-3 comprises the following steps:

Step 3-3-1: Use the multidimensional Lagrange interpolation method to calculate the voltage limit probability under the actual operating state of the node load, including:

Suppose E(S), E(P _eqi ), σ(P _eqi ), E(Q _eqi ), σ(Q _eqi ) find the downlink adjacent numbers in the offline database as E ⁰ (S), E ⁰ (P _eqi ),σ ⁰ (P _eqi ),E ⁰ (Q _eqi ),σ ⁰ (Q _eqi ), the uplink adjacent numbers found in the offline database are E ¹ (S),E ¹ (P _eqi ),σ ¹ (P _eqi ),E ¹ (Q _eqi ),σ ¹ (Q _eqi ), then the probability f of the voltage exceeding the limit corresponding to the adjacent number is obtained:

Among them, j ₁ , j ₂ ,..., j ₅ represent the state indexes of E(S), E(P _eqi ), σ(P _eqi ), E(Q _eqi ), σ(Q _eqi ) respectively, and the values are Both are 0 or 1, namely:

When j ₁ ,j ₂ ,...,j ₅ take 0, Respectively represent the downlink adjacent numbers of E(S), E(P _eqi ), σ(P _eqi ), E(Q _eqi ), and σ(Q _eqi );

When j ₁ ,j ₂ ,...,j ₅ take 1, Respectively represent the uplink adjacent numbers of E(S), E(P _eqi ), σ(P _eqi ), E(Q _eqi ), σ(Q _eqi );

use Indicates the j _1st interpolation basis function of E(S), that is, when j ₁ is 0, Indicates the 0th interpolation basis function l ₀ (E(S)) of E(S); when j ₁ is 1, The first interpolation basis function l ₁ (E(S)) representing E(S); l ₀ (E(S)) and l ₁ (E(S)) are expressed as:

use Indicates the j _2th interpolation basis function of E(P _eqi ), that is, when j ₂ is 0, Indicates the 0th interpolation basis function l ₀ (E(P _eqi )) of E(P _eqi ); when j ₂ is 1, The first interpolation basis function l ₁ (E(P _eqi )) representing E(P _eqi ); l ₀ (E(P _eqi )) and l ₁ (E(P _eqi )) are expressed as:

use Indicates the jth _3rd interpolation basis function of σ(P _eqi ), that is, when j ₃ is 0, Indicates the 0th interpolation basis function l ₀ (σ(P _eqi )) of σ(P _eqi ); when j ₃ is 1, The first interpolation basis function l ₁ (σ(P _eqi )) representing σ(P _eqi ); l ₀ (σ(P _eqi )) and l ₁ (σ(P _eqi )) are expressed as:

use Indicates the j _4th interpolation basis function of E(Q _eqi ), that is, when j ₄ is 0, Indicates the 0th interpolation basis function l ₀ (E(Q _eqi )) of E(Q _eqi ); when j ₄ is 1, The first interpolation basis function l ₁ (E(Q _eqi )) representing E(Q _eqi ); l ₀ (E(Q _eqi )) and l ₁ (E(Q _eqi )) are expressed as:

use Indicates the j _5th interpolation basis function of σ(Q _eqi ), that is, when j ₅ is 0, Indicates the 0th interpolation basis function l ₀ (σ(Q _eqi )) of σ(Q _eqi ); when j ₅ is 1, The first interpolation basis function l ₁ (σ(Q _eqi )) representing σ(Q _eqi ); l ₀ (σ(Q _eqi )) and l ₁ (σ(Q _eqi )) are expressed as:

Therefore, the probability of voltage exceeding the limit under the actual operating state of the node load is obtained, as follows:

Among them, f(E(S),E(P _eqi ),σ(P _eqi ),E(Q _eqi ),σ(Q _eqi )) represent the voltage limit probability under the actual operating state of the node load;

Step 3-3-2: According to f(E(S),E(P _eqi ),σ(P _eqi ),E(Q _eqi ),σ(Q _eqi )), analyze the voltage over-limit risk, specifically: The greater the f(E(S),E(P _eqi ),σ(P _eqi ),E(Q _eqi ),σ(Q _eqi )), the greater the risk of voltage exceeding the limit.

Compared with the closest prior art, the technical solution provided by the present invention has the following beneficial effects:

1) The present invention uses the node equivalent method to simplify the operating state parameters of the active distribution network considering the random characteristics of the load and photovoltaic system, and uses the equivalent load probability model of a single node to characterize the influence of the overall system load comprehensive action on the node voltage ;

2) The present invention utilizes the characteristics that the number of equivalent state parameters of each node after simplification is small and can characterize the comprehensive effect of various operating states of the system on the node voltage, and proposes that each equivalent state parameter in the active distribution network can be selected according to the characteristics of the nodes. The discrete state of nodes is used for offline calculation and corresponding database is generated to provide reference calculation samples for online rapid analysis;

3) The present invention proposes that in the actual operation of the distribution network, the node equivalent principle is used to calculate the corresponding random parameters of each node, and the adjacent values can be searched in the offline database to form multiple sets of discrete states to perform fast multi-dimensional Lagrange interpolation method Compared with the direct solution method using various stochastic power flow methods and considering multiple random variables at the same time, this method is more conducive to fast online analysis and calculation, and has higher accuracy;

4) The present invention effectively solves the problem of quickly and accurately calculating the voltage over-limit probability of each node of the active distribution network during actual operation.

Description of drawings

Fig. 1 is a flow chart of calculating the probability of voltage exceeding the limit of each equivalent node in a discrete state by using the theorem of large numbers in an embodiment of the present invention;

Fig. 2 is a flow chart of the calculation of the voltage over-limit probability under the actual operating state of the node load using the multi-dimensional Lagrange interpolation method in the embodiment of the present invention.

detailed description

The present invention will be described in further detail below in conjunction with the accompanying drawings.

The invention provides a node equivalent-based active distribution network voltage overrun risk analysis method, which uses a method combining off-line calculation and online analysis to solve the problem of quickly and accurately calculating the voltage overrun of each node in the distribution network during actual operation A question of probability.

(1) Simplify the operating state parameters of the distribution system considering the random characteristics of loads and distributed power sources, making it conducive to the selection of typical states during offline calculations and the mapping of actual operating states during online analysis;

(2) According to the simplified operating state parameters of the power distribution system, through the selection of typical discrete states and the random power flow calculation based on the simulation method, an offline typical state and the analysis result database of voltage exceeding the limit probability are formed, which is fast for online operation. Computing lays the foundation;

(3) According to the node equivalent principle, the actual operating characteristics are equivalent to the simplified operating parameters, and the adjacent values of each equivalent operating parameter are searched in the offline database, and finally the actual operating voltage is quickly calculated by multi-dimensional interpolation. limited probability.

The present invention provides a node equivalent-based active distribution network voltage transgression risk analysis method, the analysis method includes the following steps:

Step 1: Establish the node equivalent load probability model, and combine the photovoltaic system light intensity stochastic model to establish the equivalent state model of the active distribution network;

Step 2: Perform stochastic power flow calculation on the discrete state of each equivalent node, and calculate the voltage limit probability of each equivalent node in the discrete state according to the stochastic power flow result;

Step 3: Find the adjacent values of the node equivalent state parameters in the actual operating state of the node load in the offline database, and calculate the voltage limit probability under the actual operating state of the node load.

Described step 1 comprises the following steps:

Step 1-1: Select the maximum load state of each node in the active distribution network, and establish a node equivalent load probability model;

Step 1-2: Combining with the stochastic model of photovoltaic system light intensity, establish the equivalent state model of active distribution network.

In the step 1-1, establishing a node equivalent load probability model includes:

Assuming that node h and node k are any two adjacent nodes, node h and node k form a line hk, there are:

in, Denotes the voltage drop vector between node h and node k, Represents the current vector of the line hk, R _hk represents the resistance of the line hk, X _hk represents the reactance of the line hk, Indicates the node k potential vector, Indicates the complex power flowing through node k;

Neglecting the line loss, then Expressed as:

Among them, j=1,2,...,N _k , N _k represents the collection of all nodes after node k in the active distribution network viewed from the head end of the line hk, Indicates the load complex power of node j;

suppose Represents the rated voltage vector of the active distribution network, E _n represents the rated voltage vector magnitude of the active distribution network, so Also expressed as:

in, express the conjugate of Indicates the impedance vector of the line hk;

Therefore, for any equivalent node i in the active distribution network, there are:

in, Indicates the voltage drop vector between the equivalent node i and the bus in the active distribution network, L _i represents the set of all lines between the equivalent node i and the bus in the active distribution network, express the conjugate;

If there is only equivalent node i with load in the active distribution network, then It can also be expressed as:

in, Indicates the sum of the impedance between the equivalent node i and the bus in the active distribution network, express the conjugate of Indicates the complex power of the equivalent node i;

Due to the random fluctuation of the load power, the short-term fluctuations of active power and reactive power of each node load satisfy the normal distribution, so it can be obtained from equations (5) and (6):

and have:

Among them, a _hk means The real part of b _hk means The imaginary part of ; P _k represents the sum of active loads of all nodes after node k in the active distribution network, namely P _j represents the active load of node j; Q _k represents the sum of reactive loads of all nodes after node k in the active distribution network, namely Q _j represents the reactive load of node j;

Then, from the linear law of normal distribution, we can get:

Among them, E(P _eqi ) represents the equivalent active load expectation of equivalent node i, E(Q _eqi ) represents the equivalent reactive load expectation of equivalent node i, P _eqi represents the equivalent active load of equivalent node i, Q _eqi represents the equivalent reactive load of equivalent node i, E(P _j ) represents the expected active load of node j, and E(Q _j ) represents the expected reactive load of node j;

Since formula (10) does not satisfy the independence of random variables, it is transformed into:

and have:

Wherein, N _node represents the set of load nodes in the active distribution network, m=1, 2,..., N _node ; express the conjugate of Represents the complex power of the load node m; L _m represents the collection of all lines between the bus and the _intersection point when the line where the load node m is located and the nearest intersection point to the load node m exists; P _m represents the active load of the load node m, Q _m represents the reactive load of load node m; c _m and d _m represent The real and imaginary parts of ;

So there are:

Among them, σ(P _eqi ) represents the standard deviation of the equivalent active load of the equivalent node i, σ(Q _eqi ) represents the standard deviation of the equivalent reactive load of the equivalent node i, and D(P _eqi ) represents the standard deviation of the equivalent node i Equivalent active load variance, D(Q _eqi ) represents the equivalent reactive load variance of equivalent node i, D(P _m ) represents the active load variance of load node m, D(Q _m ) represents the reactive power of load node m load variance.

In the step 1-2, in the stochastic model of the photovoltaic system light intensity, the sun light intensity obeys the Beta distribution, and the sun light intensity expectation is represented by E(S), so the equivalent state model of the active distribution network is expressed as:

{E(S),E(P _eqi ),σ(P _eqi ),E(Q _eqi ),σ(Q _eqi )} (14)

Among them, σ(P _eqi ) represents the standard deviation of the equivalent active load of the equivalent node i, σ(Q _eqi ) represents the standard deviation of the equivalent reactive load of the equivalent node i, and E(P _eqi ) represents the standard deviation of the equivalent node i The equivalent active load expectation, E(Q _eqi ) represents the equivalent reactive load expectation of the equivalent node i.

As shown in Figure 1, the step 2 includes the following steps:

Step 2-1: Select the discrete state of each equivalent node in the active distribution network;

Step 2-2: Use Latin hypercube sampling to perform stochastic power flow calculations on the discrete states of each equivalent node, and obtain stochastic power flow results;

Step 2-3: According to the results of random power flow, and using the theorem of large numbers to calculate the probability of voltage exceeding the limit of each equivalent node in a discrete state;

Step 2-4: Save the voltage limit probability in the discrete state of each equivalent node to the offline database.

As shown in Figure 2, the step 3 includes the following steps:

Step 3-1: Obtain the actual operating status of each node load and the actual operating status of the photovoltaic system;

Step 3-2: Find the adjacent value of the node equivalent state parameter under the actual running state of the node load in the offline database;

Step 3-3: Use the multidimensional Lagrange interpolation method to calculate the probability of voltage exceeding the limit under the actual operating state of the node load, and analyze the risk of voltage exceeding the limit.

In the step 3-2, the node equivalent state parameters include the solar illumination intensity expectation E(S), the equivalent active load expectation E(P _eqi ) of the equivalent node i, and the equivalent active load standard deviation of the equivalent node i σ(P _eqi ), the equivalent reactive load expectation E(Q _eqi ) of the equivalent node i and the standard deviation σ(Q _eqi ) of the equivalent reactive load of the equivalent node i.

Said step 3-3 comprises the following steps:

Step 3-3-1: Use the multidimensional Lagrange interpolation method to calculate the voltage limit probability under the actual operating state of the node load, including:

Suppose E(S), E(P _eqi ), σ(P _eqi ), E(Q _eqi ), σ(Q _eqi ) find the downlink adjacent numbers in the offline database as E ⁰ (S), E ⁰ (P _eqi ),σ ⁰ (P _eqi ),E ⁰ (Q _eqi ),σ ⁰ (Q _eqi ), the uplink adjacent numbers found in the offline database are E ¹ (S),E ¹ (P _eqi ),σ ¹ (P _eqi ),E ¹ (Q _eqi ),σ ¹ (Q _eqi ), then the probability f of the voltage exceeding the limit corresponding to the adjacent number is obtained:

Among them, j ₁ , j ₂ ,..., j ₅ represent the state indexes of E(S), E(P _eqi ), σ(P _eqi ), E(Q _eqi ), σ(Q _eqi ) respectively, and the values are Both are 0 or 1, namely:

When j ₁ ,j ₂ ,...,j ₅ take 0, Respectively represent the downlink adjacent numbers of E(S), E(P _eqi ), σ(P _eqi ), E(Q _eqi ), and σ(Q _eqi );

When j ₁ ,j ₂ ,...,j ₅ take 1, Respectively represent the uplink adjacent numbers of E(S), E(P _eqi ), σ(P _eqi ), E(Q _eqi ), σ(Q _eqi );

use Indicates the j _1st interpolation basis function of E(S), that is, when j ₁ is 0, Indicates the 0th interpolation basis function l ₀ (E(S)) of E(S); when j ₁ is 1, The first interpolation basis function l ₁ (E(S)) representing E(S); l ₀ (E(S)) and l ₁ (E(S)) are expressed as:

use Indicates the j _2th interpolation basis function of E(P _eqi ), that is, when j ₂ is 0, Indicates the 0th interpolation basis function l ₀ (E(P _eqi )) of E(P _eqi ); when j ₂ is 1, The first interpolation basis function l ₁ (E(P _eqi )) representing E(P _eqi ); l ₀ (E(P _eqi )) and l ₁ (E(P _eqi )) are expressed as:

use Indicates the jth _3rd interpolation basis function of σ(P _eqi ), that is, when j ₃ is 0, Indicates the 0th interpolation basis function l ₀ (σ(P _eqi )) of σ(P _eqi ); when j ₃ is 1, The first interpolation basis function l ₁ (σ(P _eqi )) representing σ(P _eqi ); l ₀ (σ(P _eqi )) and l ₁ (σ(P _eqi )) are expressed as:

use Indicates the j _4th interpolation basis function of E(Q _eqi ), that is, when j ₄ is 0, Indicates the 0th interpolation basis function l ₀ (E(Q _eqi )) of E(Q _eqi ); when j ₄ is 1, The first interpolation basis function l ₁ (E(Q _eqi )) representing E(Q _eqi ); l ₀ (E(Q _eqi )) and l ₁ (E(Q _eqi )) are expressed as:

use Indicates the j _5th interpolation basis function of σ(Q _eqi ), that is, when j ₅ is 0, Indicates the 0th interpolation basis function l ₀ (σ(Q _eqi )) of σ(Q _eqi ); when j ₅ is 1, The first interpolation basis function l ₁ (σ(Q _eqi )) representing σ(Q _eqi ); l ₀ (σ(Q _eqi )) and l ₁ (σ(Q _eqi )) are expressed as:

Therefore, the probability of voltage exceeding the limit under the actual operating state of the node load is obtained, as follows:

Among them, f(E(S),E(P _eqi ),σ(P _eqi ),E(Q _eqi ),σ(Q _eqi )) represent the voltage limit probability under the actual operating state of the node load;

Step 3-3-2: According to f(E(S),E(P _eqi ),σ(P _eqi ),E(Q _eqi ),σ(Q _eqi )), analyze the voltage over-limit risk, specifically: The greater the f(E(S),E(P _eqi ),σ(P _eqi ),E(Q _eqi ),σ(Q _eqi )), the greater the risk of voltage exceeding the limit.

Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Those of ordinary skill in the art can still modify or equivalently replace the specific implementation methods of the present invention with reference to the above embodiments. Any modifications or equivalent replacements departing from the spirit and scope of the present invention are within the protection scope of the claims of the pending application of the present invention.

Claims (8)

1. An active power distribution network voltage out-of-limit risk analysis method based on node equivalence is characterized by comprising the following steps: the analysis method comprises the following steps:

step 1: establishing a node equivalent load probability model, and establishing an equivalent state model of the active power distribution network by combining a photovoltaic system illumination intensity random model;

step 2: carrying out random load flow calculation on the discrete state of each equivalent node, and calculating the voltage out-of-limit probability of each equivalent node in the discrete state according to the random load flow result;

and step 3: and searching the adjacent values of the node equivalent state parameters in the actual running state of the node load in an offline database, and calculating the voltage out-of-limit probability in the actual running state of the node load.

2. The node equivalence-based active distribution network voltage out-of-limit risk analysis method according to claim 1, characterized in that: the step 1 comprises the following steps:

step 1-1: selecting the maximum load state of each node in the active power distribution network, and establishing a node equivalent load probability model;

step 1-2: and establishing an equivalent state model of the active power distribution network by combining a random model of the illumination intensity of the photovoltaic system.

3. The node equivalence-based active distribution network voltage out-of-limit risk analysis method according to claim 2, characterized in that: in the step 1-1, establishing a node equivalent load probability model includes:

assuming that the node h and the node k are any two adjacent nodes, the node h and the node k form a line hk, which has:

${\stackrel{\·}{V}}_{hk}={\stackrel{\·}{I}}_{hk}(R_{hk}+{\mathrm{jX}}_{hk})={\left(\frac{{\stackrel{\‾}{S}}_k}{{\stackrel{\·}{E}}_k}\right)}^{*}(R_{hk}+{\mathrm{jX}}_{hk})---\left(1\right)$

wherein,representing the vector of the voltage drop between node h and node k,representing the current vector, R, of the line hk_hkRepresenting the resistance, X, of the line hk_hkThe reactance of the line hk is shown,a vector of the potential of the node k is represented,represents the complex power flowing through node k;

neglecting the line loss, thenExpressed as:

${\stackrel{\‾}{S}}_k=\underset{j\∈N_k}{\Σ}{\stackrel{\‾}{S}}_j---\left(2\right)$

wherein j is 1,2, …, N_k，N_kRepresenting the set of all nodes looking into the active distribution network from the head end of line hk behind node k,represents the load complex power of node j;

suppose that Representing the rated voltage vector of the active distribution network, E_nRepresenting the magnitude of the rated voltage vector of the active distribution network, thusAnd is represented as:

${\stackrel{\·}{V}}_{hk}=\frac{1}{E_n}{\stackrel{\‾}{S}}_k^{*}{\stackrel{\·}{Z}}_{hk}=\frac{{\stackrel{\‾}{S}}_k^{*}}{E_n}(R_{hk}+{\mathrm{jX}}_{hk})---\left(3\right)$

wherein,to representThe conjugate of (a) to (b),represents the impedance vector of line hk;

therefore, for any equivalent node i in the active power distribution network, there are:

${\stackrel{\·}{V}}_{0i}=\underset{hk\∈L_i}{\Σ}{\stackrel{\·}{V}}_{hk}=\underset{hk\∈L_i}{\Σ}\[\frac{{\stackrel{\·}{Z}}_{hk}}{E_n}\left(\underset{j\∈N_k}{\Σ}{\stackrel{\‾}{S}}_j^{*}\right)\]---\left(4\right)$

wherein,representing the vector of the voltage drop between the equivalent node i and the bus in the active distribution network, L_iRepresenting the set of all lines between the equivalent node i and the bus in the active distribution network,to representConjugation of (1);

if only the equivalent node i in the active power distribution network is loaded, the load is reducedAnd can be represented as:

${\stackrel{\·}{V}}_{0i}=\frac{{\stackrel{\·}{Z}}_{0i}{\stackrel{\‾}{S}}_{eqi}^{*}}{E_n}---\left(5\right)$

wherein,representing the sum of the impedances between the equivalent node i and the busbars in the active distribution network,to representThe conjugate of (a) to (b),representing the complex power of the equivalent node i;

since the load power has random fluctuation, the active power short-term fluctuation and the reactive power short-term fluctuation of each node load both satisfy the normal distribution, and then are obtained by the following equations (5) and (6):

${\stackrel{\‾}{S}}_{eqi}^{*}=\underset{hk\∈L_i}{\Σ}\[\frac{{\stackrel{\·}{Z}}_{hk}}{{\stackrel{\·}{Z}}_{0i}}\left(\underset{j\∈N_k}{\Σ}{\stackrel{\‾}{S}}_j^{*}\right)\]=\underset{hk\∈L_i}{\Σ}\[(a_{hk}{P}_k+b_{hk}{Q}_k)+j(b_{hk}{P}_k-a_{hk}{Q}_k)\]---\left(6\right)$

and has the following components:

$\frac{{\stackrel{\·}{Z}}_{hk}}{{\stackrel{\·}{Z}}_{0i}}=a_{hk}+{\mathrm{jb}}_{hk}---\left(7\right)$

wherein, a_hkTo representThe real part of (a) is,b_hkto representAn imaginary part of (d); p_kRepresenting the sum of the active loads of all nodes following node k in the active distribution network, i.e.P_jRepresenting the active load of node j; q_kRepresenting the sum of the reactive loads of all nodes after node k in the active distribution network, i.e.Q_jRepresenting the reactive load of node j;

from the linear law of normal distribution then:

$E\left(P_{eqi}\right)=\underset{hk\∈L_i}{\Σ}\[a_{hk}\underset{j\∈N_k}{\Σ}E\left(P_j\right)+b_{hk}\underset{j\∈N_k}{\Σ}E\left(Q_j\right)\]---\left(8\right)$

$E\left(Q_{eqi}\right)=\underset{hk\∈L_i}{\Σ}\[a_{hk}\underset{j\∈N_k}{\Σ}E\left(Q_j\right)-b_{hk}\underset{j\∈N_k}{\Σ}E\left(P_j\right)\]---\left(9\right)$

wherein, E (P)_eqi) Representing the equivalent active load expectation, E (Q), of the equivalent node i_eqi) Representing the equivalent reactive load expectation, P, of the equivalent node i_eqiRepresenting the equivalent active load, Q, of an equivalent node i_eqiRepresenting the equivalent reactive load of the equivalent node i, E (P)_j) Representing the active load expectation of node j, E (Q)_j) Represents the reactive load expectation of node j;

since equation (10) does not satisfy the random variable independence, it is transformed into:

${\stackrel{\‾}{S}}_{eqi}^{*}=\frac{\underset{m\∈N_{node}}{\Σ}\[{\stackrel{\‾}{S}}_m^{*}\underset{hk\∈L_m}{\Σ}{\stackrel{\·}{Z}}_{hk}\]}{{\stackrel{\·}{Z}}_{0i}}=\underset{m\∈N_{node}}{\Σ}\[\left(c_m{P}_m+d_m{Q}_m\right)+j\left(d_m{P}_m-c_m{Q}_m\right)\]---\left(10\right)$

and has the following components:

$\frac{\underset{hk\∈L_m}{\Σ}{\stackrel{\·}{Z}}_{hk}}{{\stackrel{\·}{Z}}_{0i}}=c_m+{\mathrm{jd}}_m---\left(11\right)$

wherein N is_nodeRepresenting a set of load nodes in the active distribution network, m being 1,2, …, N_node；To representThe conjugate of (a) to (b),representing the complex power of the load node m; l is_mIndicates the line and L of the load node m_iWhen the intersection point which is closest to the load node m exists, all lines from the bus to the intersection point are collected; p_mRepresenting the active load, Q, of the load node m_mRepresenting the reactive load of the load node m; c. C_mAnd d_mRespectively representThe real and imaginary parts of (c);

thus, there are:

$\mathrm{\σ}\left(P_{eqi}\right)=\sqrt{D\left(P_{eqi}\right)}=\sqrt{\underset{m\∈N_{node}}{\Σ}\[c_m^{2}D\left(P_m\right)+d_m^{2}D\left(Q_m\right)\]}---\left(12\right)$

$\mathrm{\σ}\left(Q_{eqi}\right)=\sqrt{D\left(Q_{eqi}\right)}=\sqrt{\underset{m\∈N_{node}}{\Σ}\[d_m^{2}D\left(P_m\right)+c_m^{2}D\left(Q_m\right)\]}---\left(13\right)$

wherein, σ (P)_eqi) Represents the equivalent active load standard deviation, sigma (Q) of the equivalent node i_eqi) Represents the equivalent reactive load standard deviation, D (P) of the equivalent node i_eqi) Represents the equivalent active load variance, D (Q), of the equivalent node i_eqi) Represents the equivalent reactive load variance, D (P), of the equivalent node i_m) Representing the active load variance, D (Q), of the load node m_m) Representing the reactive load variance of load node m.

4. The node equivalence-based active distribution network voltage out-of-limit risk analysis method according to claim 3, wherein: in the step 1-2, in the photovoltaic system illumination intensity random model, the solar illumination intensity obeys Beta distribution, and the solar illumination intensity is expected to be expressed by e(s), so that the active power distribution network equivalent state model is expressed as:

{E(S),E(P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi)} (14)

wherein, σ (P)_eqi) Represents the equivalent active load standard deviation, sigma (Q) of the equivalent node i_eqi) Represents the equivalent reactive load standard deviation, E (P), of the equivalent node i_eqi) Representing the equivalent active load expectation, E (Q), of the equivalent node i_eqi) Representing the equivalent reactive load expectation of the equivalent node i.

5. The node equivalence-based active distribution network voltage out-of-limit risk analysis method according to claim 1, characterized in that: the step 2 comprises the following steps:

step 2-1: selecting discrete states of equivalent nodes in the active power distribution network;

step 2-2: performing random load flow calculation on the discrete state of each equivalent node by adopting Latin hypercube sampling to obtain a random load flow result;

step 2-3: calculating the voltage out-of-limit probability of each equivalent node in a discrete state by adopting a majority theorem according to the random load flow result;

step 2-4: and storing the voltage out-of-limit probability of each equivalent node in a discrete state to an offline database.

6. The node equivalence-based active distribution network voltage out-of-limit risk analysis method according to claim 1, characterized in that: the step 3 comprises the following steps:

step 3-1: acquiring the actual running state of each node load and the actual running state of the photovoltaic system;

step 3-2: searching an adjacent value of the node equivalent state parameter in an actual running state of the node load in an offline database;

step 3-3: and calculating the voltage out-of-limit probability of the node load in the actual running state by adopting a multidimensional Lagrange interpolation method, and analyzing the voltage out-of-limit risk.

7. The node equivalence-based active distribution network voltage out-of-limit risk analysis method according to claim 6, wherein: in the step 3-2, the node equivalent state parameters include the solar illumination intensity expectation E (S), the equivalent active load expectation E (P) of the equivalent node i_eqi) And the equivalent active load standard deviation sigma (P) of the equivalent node i_eqi) Equivalent reactive load expectation E (Q) of equivalent node i_eqi) And the equivalent reactive load standard deviation sigma (Q) of the equivalent node i_eqi)。

8. The node equivalence-based active distribution network voltage out-of-limit risk analysis method according to claim 7, wherein: the step 3-3 comprises the following steps:

step 3-3-1: calculating the voltage out-of-limit probability under the actual operation state of the node load by adopting a multidimensional Lagrange interpolation method, wherein the method comprises the following steps:

assume E (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The downlink adjacent numbers found in the off-line database are respectively E⁰(S),E⁰(P_eqi),σ⁰(P_eqi),E⁰(Q_eqi),σ⁰(Q_eqi) In an off-line databaseThe found uplink adjacent numbers are respectively E¹(S),E¹(P_eqi),σ¹(P_eqi),E¹(Q_eqi),σ¹(Q_eqi) Then, the voltage out-of-limit probability f corresponding to the adjacent number is obtained, including:

$f=f\left(E^{j_1}\right(S),E^{j_2}(P_{eqi}),{\mathrm{\σ}}^{j_3}(P_{eqi}),E^{j_4}(Q_{eqi}),{\mathrm{\σ}}^{j_5}(Q_{eqi}\left)\right)---\left(15\right)$

wherein j is₁,j₂,...,j₅Respectively represent E (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The values of the state index of (1) are both 0 or 1, namely:

j₁,j₂,...,j₅when the value of 0 is taken out,respectively represent E (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The downlink adjacency number of (2);

j₁,j₂,...,j₅when the number 1 is taken out, the number 1,respectively represent E (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The uplink adjacency number of (2);

by usingJ denotes E (S)₁An interpolation basis function, i.e. j₁When the value of 0 is taken out,0 th interpolation basis function l representing E (S)₀(E(S))；j₁When the number 1 is taken out, the number 1,1 st interpolation basis function l representing E (S)₁(E(S))；l₀(E (S)) and l₁(E (S)) are respectively represented as:

$l_0\left(E\right(S\left)\right)=\frac{E\left(S\right)-E^1\left(S\right)}{E^0\left(S\right)-E^1\left(S\right)}---\left(16\right)$

$l_1\left(E\right(S\left)\right)=\frac{E\left(S\right)-E^0\left(S\right)}{E^1\left(S\right)-E^0\left(S\right)}---\left(17\right)$

by usingRepresents E (P)_eqi) J (d) of₂An interpolation basis function, i.e. j₂When the value of 0 is taken out,represents E (P)_eqi) 0 th interpolation basis function l₀(E(P_eqi))；j₂When the number 1 is taken out, the number 1,represents E (P)_eqi) 1 st interpolation basis function l₁(E(P_eqi))；l₀(E(P_eqi) And l)₁(E(P_eqi) Respectively expressed as:

$l_0\left(E\right(P_{eqi}\left)\right)=\frac{E\left(P_{eqi}\right)-E^1\left(P_{eqi}\right)}{E^0\left(P_{eqi}\right)-E^1\left(P_{eqi}\right)}---\left(18\right)$

$l_1\left(E\right(P_{eqi}\left)\right)=\frac{E\left(P_{eqi}\right)-E^0\left(P_{eqi}\right)}{E^1\left(P_{eqi}\right)-E^0\left(P_{eqi}\right)}---\left(19\right)$

by usingRepresents sigma (P)_eqi) J (d) of₃An interpolation basis function, i.e. j₃When the value of 0 is taken out,represents sigma (P)_eqi) 0 th interpolation basis function l₀(σ(P_eqi))；j₃When the number 1 is taken out, the number 1,represents sigma (P)_eqi) 1 st interpolation basis function l₁(σ(P_eqi))；l₀(σ(P_eqi) And l)₁(σ(P_eqi) Respectively expressed as:

$l_0\left(\mathrm{\σ}\right(P_{eqi}\left)\right)=\frac{\mathrm{\σ}\left(P_{eqi}\right)-{\mathrm{\σ}}^1\left(P_{eqi}\right)}{{\mathrm{\σ}}^0\left(P_{eqi}\right)-{\mathrm{\σ}}^1\left(P_{eqi}\right)}---\left(20\right)$

$l_1\left(\mathrm{\σ}\right(P_{eqi}\left)\right)=\frac{\mathrm{\σ}\left(P_{eqi}\right)-{\mathrm{\σ}}^0\left(P_{eqi}\right)}{{\mathrm{\σ}}^1\left(P_{eqi}\right)-{\mathrm{\σ}}^0\left(P_{eqi}\right)}---\left(21\right)$

by usingRepresents E (Q)_eqi) J (d) of₄An interpolation basis function, i.e. j₄When the value of 0 is taken out,represents E (Q)_eqi) 0 th interpolation basis function l₀(E(Q_eqi))；j₄When the number 1 is taken out, the number 1,represents E (Q)_eqi) 1 st interpolation basis function l₁(E(Q_eqi))；l₀(E(Q_eqi) And l)₁(E(Q_eqi) Respectively expressed as:

$l_0\left(E\right(Q_{eqi}\left)\right)=\frac{E\left(Q_{eqi}\right)-E^1\left(Q_{eqi}\right)}{E^0\left(Q_{eqi}\right)-E^1\left(Q_{eqi}\right)}---\left(22\right)$

$l_1\left(E\right(Q_{eqi}\left)\right)=\frac{E\left(Q_{eqi}\right)-E^0\left(Q_{eqi}\right)}{E^1\left(Q_{eqi}\right)-E^0\left(Q_{eqi}\right)}---\left(23\right)$

by usingRepresents sigma (Q)_eqi) J (d) of₅An interpolation basis function, i.e. j₅When the value of 0 is taken out,represents sigma (Q)_eqi) 0 th interpolation basis function l₀(σ(Q_eqi))；j₅When the number 1 is taken out, the number 1,represents sigma (Q)_eqi) 1 st interpolation basis function l₁(σ(Q_eqi))；l₀(σ(Q_eqi) And l)₁(σ(Q_eqi) Respectively expressed as:

$l_0\left(\mathrm{\σ}\right(Q_{eqi}\left)\right)=\frac{\mathrm{\σ}\left(Q_{eqi}\right)-{\mathrm{\σ}}^1\left(Q_{eqi}\right)}{{\mathrm{\σ}}^0\left(Q_{eqi}\right)-{\mathrm{\σ}}^1\left(Q_{eqi}\right)}---\left(24\right)$

$l_1\left(\mathrm{\σ}\right(Q_{eqi}\left)\right)=\frac{\mathrm{\σ}\left(Q_{eqi}\right)-{\mathrm{\σ}}^0\left(Q_{eqi}\right)}{{\mathrm{\σ}}^1\left(Q_{eqi}\right)-{\mathrm{\σ}}^0\left(Q_{eqi}\right)}---\left(25\right)$

therefore, the voltage out-of-limit probability under the actual operation state of the node load is obtained by the following steps:

$\begin{array}{c}f\left(E\left(S\right),E\left(P_{eqi}\right),\mathrm{\σ}\left(P_{eqi}\right),E\left(Q_{eqi}\right),\mathrm{\σ}\left(Q_{eqi}\right)\right)=\\ \underset{j_1=0}{\overset{1}{\Σ}}\underset{j_2=0}{\overset{1}{\Σ}}...\underset{j_5=0}{\overset{1}{\Σ}}\left[\begin{array}{c}{l}_{j_1}\left(E\left(S\right)\right)\×l_{j_2}\left(E\left(P_{eqi}\right)\right)\×l_{j_3}\left(\mathrm{\σ}\left(P_{eqi}\right)\right)\×l_{j_4}\left(E\left(Q_{eqi}\right)\right)\×l_{j_5}\left(\mathrm{\σ}\left(Q_{eqi}\right)\right)\\ \×f\left(E^{j_1}\left(S\right),E^{j_2}\left(P_{eqi}\right),{\mathrm{\σ}}^{j_3}\left(P_{eqi}\right),E^{j_4}\left(Q_{eqi}\right),{\mathrm{\σ}}^{j_5}\left(Q_{eqi}\right)\right)\end{array}\right]\end{array}---\left(26\right)$

wherein f (E), (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) Represents the voltage out-of-limit probability under the actual operating state of the node load;

step 3-3-2: according to f (E), (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) Analysis of voltage out-of-limit risks, specifically: f (E), (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The greater the voltage violation risk.